from collections import Counter

def find_parity_outliers(nums):
  return [
    x for x in nums
    if x % 2 != Counter([n % 2 for n in nums]).most_common()[0][0]
  ]

find_parity_outliers([1, 2, 3, 4, 6]) # [1, 3]

def key_of_min(d):
  return min(d, key = d.get)

key_of_min({'a':4, 'b':0, 'c':13}) # b

def sum_of_powers(end, power = 2, start = 1):
  return sum([(i) ** power for i in range(start, end + 1)])

sum_of_powers(10) # 385
sum_of_powers(10, 3) # 3025
sum_of_powers(10, 3, 5) # 2925

# @return a list of strings, [s1, s2]
def letterCombinations(self, digits):
    if '' == digits: return []
    kvmaps = {
        '2': 'abc',
        '3': 'def',
        '4': 'ghi',
        '5': 'jkl',
        '6': 'mno',
        '7': 'pqrs',
        '8': 'tuv',
        '9': 'wxyz'
    }
    return reduce(lambda acc, digit: [x + y for x in acc for y in kvmaps[digit]], digits, [''])

#Sets
U = {0,1,2,3,4,5,6,7,8,9}
P = {1,2,3,4}
Q = {4,5,6}
R = {3,4,6,8,9}

def set2bits(xs,us) :
    bs=[]
    for x in us :
        if x in xs :
            bs.append(1)
        else:
            bs.append(0)
    assert len(us) == len(bs)
    return bs

def union(set1,set2) :
    finalSet = set()
    bitList1 = set2bits(set1, U)
    bitList2 = set2bits(set2, U)

    for i in range(len(U)) :
        if(bitList1[i] or bitList2[i]) :
            finalSet.add(i)

    return finalSet

def intersection(set1,set2) :
    finalSet = set()
    bitList1 = set2bits(set1, U)
    bitList2 = set2bits(set2, U)

    for i in range(len(U)) :
        if(bitList1[i] and bitList2[i]) :
            finalSet.add(i)

    return finalSet

def compliment(set1) :
    finalSet = set()
    bitList = set2bits(set1, U)

    for i in range(len(U)) :
        if(not bitList[i]) :
            finalSet.add(i)

    return finalSet

def implication(a,b):
    return union(compliment(a), b)

###########################################################################################
######################         Problems 1-6         #######################################
###########################################################################################

#p \/ (q /\ r) = (p \/ q) /\ (p \/ r)
def prob1():
    return union(P, intersection(Q,R)) == intersection(union(P,Q), union(P,R))

#p /\ (q \/ r) = (p /\ q) \/ (p /\ r)
def prob2():
    return intersection(P, union(Q,R)) == union(intersection(P,Q), intersection(P,R))

#~(p /\ q) = ~p \/ ~q
def prob3():
    return compliment(intersection(P,R)) == union(compliment(P), compliment(R))

#~(p \/ q) = ~p /\ ~q
def prob4():
    return compliment(union(P,Q)) == intersection(compliment(P), compliment(Q))

#(p=>q) = (~q => ~p)
def prob5():
    return implication(P,Q) == implication(compliment(Q), compliment(P))

#(p => q) /\ (q => r)  =>  (p => r)
def prob6():
    return implication(intersection(implication(P,Q), implication(Q,R)), implication(P,R))


print("Problem 1: ", prob1())
print("Problem 2: ", prob2())
print("Problem 3: ", prob3())
print("Problem 4: ", prob4())
print("Problem 5: ", prob5())
print("Problem 6: ", prob6())

'''
Problem 1:  True
Problem 2:  True
Problem 3:  True
Problem 4:  True
Problem 5:  True
Problem 6:  {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
'''

import random

class Node:

    def __init__(self, c):

        self.left = None
        self.right = None
        self.color = c
    
    def SetColor(self,c) :
        self.color = c

    def PrintNode(self) :
        print(self.color)

def insert(s, root, i, n):
    if i < n:
        temp = Node(s[i]) 
        root = temp 
        root.left = insert(s, root.left,2 * i + 1, n) 
        root.right = insert(s, root.right,2 * i + 2, n)
    return root
  

def MakeTree(s) :
    list = insert(s,None,0,len(s))
    return list


def MakeSet() :
    s = []
    count = random.randint(7,12)
    for _ in range(count) :
        color = random.randint(0,1) == 0 and "Red" or "White"
        s.append(color)
    return s

def ChangeColor(root) :
    if (root != None) :
        if (root.color == "White") :
            root.SetColor("Red")
        ChangeColor(root.left)
        ChangeColor(root.right)


def PrintList(root) :
    if root.left != None :
        PrintList(root.left)
    else :
        root.PrintNode()
    if root.right != None :
        PrintList(root.right)
    else :
        root.PrintNode()


t1 = MakeTree(MakeSet())
print("Original Colors For Tree 1:\n")
PrintList(t1)
ChangeColor(t1)
print("New Colors For Tree 1:\n")
PrintList(t1)

t2 = MakeTree(MakeSet())
print("Original Colors For Tree 2:\n")
PrintList(t2)
ChangeColor(t2)
print("New Colors For Tree 2:\n")
PrintList(t2)

t3 = MakeTree(MakeSet())
print("Original Colors For Tree 3:\n")
PrintList(t3)
ChangeColor(t3)
print("New Colors For Tree 3:\n")
PrintList(t3)